“To-morrow will be the fifteenth birthday of the Quaternions.  They started into life full-grown on the 16th October, 1843, as I was walking with Lady Hamilton to Dublin, and came up to Brougham Bridge—­which my boys have since called Quaternion Bridge.  I pulled out a pocketbook which still exists, and made entry, on which at the very moment I felt that it might be worth my while to expend the labour of at least ten or fifteen years to come.  But then it is fair to say that this was because I felt a problem to have been at that moment solved, an intellectual want relieved which had haunted me for at least fifteen years before.

“But did the thought of establishing such a system, in which geometrically opposite facts—­namely, two lines (or areas) which are opposite in space give always a positive product—­ever come into anybody’s head till I was led to it in October, 1843, by trying to extend my old theory of algebraic couples, and of algebra as the science of pure time?  As to my regarding geometrical addition of lines as equivalent to composition of motions (and as performed by the same rules), that is indeed essential in my theory but not peculiar to it; on the contrary, I am only one of many who have been led to this view of addition.”

Pilgrims in future ages will doubtless visit the spot commemorated by the invention of Quaternions.  Perhaps as they look at that by no means graceful structure Quaternion Bridge, they will regret that the hand of some Old Mortality had not been occasionally employed in cutting the memorable inscription afresh.  It is now irrecoverably lost.

It was ten years after the discovery that the great volume appeared under the title of “Lectures on Quaternions,” Dublin, 1853.  The reception of this work by the scientific world was such as might have been expected from the extraordinary reputation of its author, and the novelty and importance of the new calculus.  His valued friend, Sir John Herschel, writes to him in that style of which he was a master:—­

“Now, most heartily let me congratulate you on getting out your book—­on having found utterance, ore rotundo, for all that labouring and seething mass of thought which has been from time to time sending out sparks, and gleams, and smokes, and shaking the soil about you; but now breaks into a good honest eruption, with a lava stream and a shower of fertilizing ashes.

“Metaphor and simile apart, there is work for a twelve-month to any man to read such a book, and for half a lifetime to digest it, and I am glad to see it brought to a conclusion.”

We may also record Hamilton’s own opinion expressed to Humphrey Lloyd:—­

“In general, although in one sense I hope that I am actually growing modest about the quaternions, from my seeing so many peeps and vistas into future expansions of their principles, I still must assert that this discovery appears to me to be as important for the middle of the nineteenth century as the discovery of fluxions was for the close of the seventeenth.”